Would anyone mind viewing the video below and telling me what DE this person is using? It looks like Gnome3 but different than I've seen implemented in Ubuntu 17.10. Would Gnome3 look like this on top of Mint? Thank you in advance.

Linux Mint 18.x have Gnome 3.18 in the repositories which will look and work a bit different. Linux Mint 19 will have the same Gnome version as Ubuntu 17.10 (because Ubuntu 18.04 on which Linux Mint 19 will be based keeps the same Gnome version as Ubuntu 17.10) and so if you were to install Gnome on Linux Mint 19 you should be able to make it look exactly like that.

Linux Mint 18.x have Gnome 3.18 in the repositories which will look and work a bit different. Linux Mint 19 will have the same Gnome version as Ubuntu 17.10 (because Ubuntu 18.04 on which Linux Mint 19 will be based keeps the same Gnome version as Ubuntu 17.10) and so if you were to install Gnome on Linux Mint 19 you should be able to make it look exactly like that.